LeanCat: A Benchmark Suite for Formal Category Theory in Lean (Part I: 1-Categories)
This addresses a gap in evaluating high-level reasoning for formal mathematics and software engineering, though it is incremental as it builds on existing benchmarks and methods.
The authors tackled the problem of measuring library-grounded abstraction in formal theorem proving by introducing LeanCat, a benchmark of 100 category-theory tasks in Lean, and found that state-of-the-art models solved only 12.0% of tasks, while their retrieval-augmented agent LeanBridge achieved 24.0% success.
While large language models (LLMs) have demonstrated impressive capabilities in formal theorem proving, current benchmarks fail to adequately measure library-grounded abstraction -- the ability to reason with high-level interfaces and reusable structures central to modern mathematics and software engineering. We introduce LeanCat, a challenging benchmark comprising 100 fully formalized category-theory tasks in Lean. Unlike algebra or arithmetic, category theory serves as a rigorous stress test for structural, interface-level reasoning. Our evaluation reveals a severe abstraction gap: the best state-of-the-art model solves only 12.0% of tasks at pass@4, with performance collapsing from 55.0% on Easy tasks to 0.0% on High-difficulty tasks, highlighting a failure in compositional generalization. To overcome this, we evaluate LeanBridge, a retrieval-augmented agent that employs a retrieve-generate-verify loop. LeanBridge achieves a peak success rate of 24.0% -- doubling the performance of the best static baseline. These results empirically demonstrate that iterative refinement and dynamic library retrieval are not merely optimizations but strict necessities for neuro-symbolic reasoning in abstract domains. LeanCat offers a compact, reusable testbed for tracking progress toward reliable, research-level formalization.